Wether in FMGo or FMPro, when logging in to an account using OAuth, the user is taken to their default web browser, which once they have signed in, takes prompts them to "Open" FileMaker. When they click ok, they are taken back to FileMaker and logged in.
This is a great advance, but still not on par with how modern apps handle OAuth logins.
Most will open an "in-app" browser window, which - without the user being prompted to do anything - closes once the user has authenticated with the OAuth provider and seamlessly carries on in the app.
For example, add a Google account in Mac system preferences, internet accounts. It will open a little window which shows the Google OAuth pages. Then closes out without any prompts once your done.